You’re correct regarding the law limiting you to one concealed pistol at a time. You would be able to have a second pistol loaded in your car but I believe you would have to unload it if it leaves the car in a concealed manner. As far as I know there is no legal avenue for carrying a loaded rifle concealed at all. A rifle carried openly can be loaded but a rifle carried concealed cannot based on my reading of the statutes.
If you’d only be transporting the gun to have it at your final destination and it doesn’t matter if it’s ready to use, why not just separate the upper and lower of an AR? It would then fit in a fairly small bag.